Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
1. Equations & Inequalities
Linear Equations
4:03 minutes
Problem 20a
Textbook Question
Textbook QuestionSolve each equation. 4[2x-(3-x)+5] = -6x - 28
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Distributive Property
The distributive property states that a(b + c) = ab + ac. This property allows us to multiply a single term by each term inside a set of parentheses. In the context of the given equation, applying the distributive property is essential to simplify the expression 4[2x - (3 - x) + 5] before solving for x.
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Combining Like Terms
Combining like terms involves adding or subtracting terms that have the same variable raised to the same power. This step is crucial in simplifying algebraic expressions and equations. In the equation provided, after applying the distributive property, it will be necessary to combine like terms to isolate the variable x effectively.
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Solving Linear Equations
Solving linear equations involves finding the value of the variable that makes the equation true. This process typically includes isolating the variable on one side of the equation through operations such as addition, subtraction, multiplication, or division. Understanding how to manipulate the equation correctly is key to arriving at the solution for x in the given problem.
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